Reduced homography based on structural redundancy of conditioned motion

Abstract

Efficient techniques of recovering the pose of an optical apparatus exploiting structural redundancies due the conditioned motion of an apparatus are disclosed. The techniques are based on determining a reduced homography consonant to the conditioned motion of the optical apparatus. The optical apparatus comprises an optical sensor on which space points are imaged as measured image points. The reduced homography is based on a reduced representation of the space points, obtained by exploiting the structural redundancy in the measured image points due to the conditioned motion. The reduced representation consonant with the conditioned motion is defined by rays in homogeneous coordinates and contained in a projective plane of the optical sensor.

The invention claimed is: 
     
       1. A method of recovering pose parameters of an optical apparatus, said method comprising the steps of:
 a) imaging a plurality of space points as measured imaged points on an optical sensor of said optical apparatus; 
 b) determining a structural redundancy in said measured image points due to a conditioned motion of said optical sensor; 
 c) employing a reduced representation of said measured image points as a plurality of rays in homogeneous coordinates in a projective plane of said optical sensor, said reduced representation being consonant with said conditioned motion; and 
 d) estimating at least one pose parameter with respect to a canonical pose of said optical apparatus by employing said reduced representation. 
 
     
     
       2. The method according to  claim 1 , wherein said optical apparatus also experiences said conditioned motion of said optical sensor. 
     
     
       3. The method according to  claim 1 , wherein said conditioned motion is constrained to a predetermined plane. 
     
     
       4. The method according to  claim 3 , wherein said conditioned motion is allowed to vary within a tolerance margin perpendicular to said arbitrary plane. 
     
     
       5. The method according to  claim 1 , further employing a reduced homography based on said reduced representation in said step of estimating of said at least one pose parameter. 
     
     
       6. The method according to  claim 5 , wherein said conditioned motion is consonant with said reduced homography. 
     
     
       7. The method according to  claim 5 , wherein said conditioned motion conforms to an orthogonal base case. 
     
     
       8. The method according to  claim 7 , wherein a mathematical formulation of said orthogonal base case is transformed to another orthogonal base case. 
     
     
       9. The method according to  claim 5 , wherein said reduced homography employs a permutation matrix of a transformation from a first orthogonal base case to a second orthogonal base case. 
     
     
       10. The method according to  claim 5 , wherein said conditioned motion is constrained to a predetermined plane. 
     
     
       11. The method according to  claim 10 , wherein said conditioned motion is allowed to vary within a tolerance margin in a direction perpendicular to said arbitrary plane. 
     
     
       12. The method according to  claim 5 , wherein said at least one pose parameter is a translation of said optical apparatus, and a measurement bias in said step of estimating is determined with respect to an auxiliary measurement of said translation. 
     
     
       13. The method according to  claim 12 , wherein said auxiliary measurement is performed utilizing at least one item selected from the group consisting of a second said optical apparatus and an auxiliary sensor. 
     
     
       14. The method according to  claim 13 , wherein said auxiliary sensor is selected from the group consisting of an optical sensor, an accelerometer, a gyro, a magnetometer, an optical flow sensor, a displacement sensor, an acoustic sensor, a Radio Frequency (RF) sensor and an inertial sensor. 
     
     
       15. The method according to  claim 12 , further filtering said at least one pose parameter based on said measurement bias. 
     
     
       16. The method according to  claim 15 , further using said filtering to determine a goodness of said step of estimating of said at least one pose parameter. 
     
     
       17. A system for recovering a pose parameter of an optical apparatus comprising:
 a) an optical sensor on which a plurality of space points are imaged as measured imaged points, said optical sensor connected to said optical apparatus; 
 b) a structural redundancy in said measured image points due to a conditioned motion of said optical sensor; 
 c) a reduced representation of said measured image points as a plurality of rays in homogeneous coordinates in a projective plane of said optical sensor, said reduced representation consonant with said conditioned motion; 
 wherein said pose parameter is estimated with respect to a canonical pose of said optical apparatus, by employing said reduced representation. 
 
     
     
       18. The system of  claim 17 , wherein said conditioned motion is confined to a predetermined plane. 
     
     
       19. The system of  claim 18 , wherein said confinement is within a tolerance margin. 
     
     
       20. The system of  claim 17 , wherein said reduced representation is used in the formulation of a reduced homography consonant with said conditioned motion. 
     
     
       21. The system of  claim 20 , wherein said reduced homography is employed in said estimation of said pose parameter.